Minimal cobordisms between thin and thick torus knots

TL;DR

This paper precisely computes the minimal cobordism distance between certain torus knots with small and large braid indices, revealing new insights into their geometric relationships and cross-sectional properties.

Contribution

It provides high-precision calculations of cobordism distances for specific torus knots and uncovers surprising properties of their cross-sections in minimal cobordisms.

Findings

Exact cobordism distances for small braid index torus knots

Identification of special cross-sectional properties in minimal cobordisms

Enhanced understanding of torus knot relationships

Abstract

We determine the locally flat cobordism distance between torus knots with small and large braid index, up to high precision. Here small means 2, 3, 4, or 6. As an application, we derive a surprising fact about torus knots that appear as cross-sections of almost minimal cobordisms between two-stranded torus knots and the trivial knot.